The strato-rotational instability of Taylor-Couette and Keplerian flows

被引:25
作者
Le Dizes, S. [1 ]
Riedinger, X. [1 ]
机构
[1] CNRS, IRPHE, UMR 6594, F-13013 Marseille, France
关键词
stratified flows; vortex instability; waves in rotating fluids; NON-AXISYMMETRICAL INSTABILITY; VORTEX; FLUIDS; MODES; DISKS;
D O I
10.1017/S0022112010002624
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The linear inviscid stability of two families of centrifugally stable rotating flows in a stably stratified fluid of constant Brunt-Vaisala frequency N is analysed by using numerical and asymptotic methods. Both Taylor-Couette and Keplerian angular velocity profiles Omega(TC) = (1 - mu)/r(2) + mu and Omega(K) =(1 - lambda)/r(2) + lambda/r(3/2) are considered between r = 1 (inner boundary) and r = d > 1 (outer boundary, or without boundary if d = infinity). The stability properties are obtained for flow parameters lambda and mu ranging from 0 to +infinity, and different values of d and N. The effect of the gap size is analysed first. By considering the potential flow (lambda = mu = 0), we show how the instability associated with a mechanism of resonance for finite-gap changes into a radiative instability when d -> infinity. Numerical results are compared with large axial wavenumber results and a very good agreement is obtained. For infinite gap (d = infinity), we show that the most unstable modes are obtained for large values of the azimuthal wavenumber for all lambda and mu. We demonstrate that their properties can be captured by performing a local analysis near the inner cylinder in the limit of both large azimuthal and axial wavenumbers. The effect of the stratification is also analysed. We show that decreasing N is stabilizing. An asymptotic analysis for small N is also performed and shown to capture the properties of the most unstable mode of the potential flow in this limit.
引用
收藏
页码:147 / 161
页数:15
相关论文
共 50 条
[41]   Influence of homogeneous magnetic fields on the flow of a ferrofluid in the Taylor-Couette system [J].
Altmeyer, S. ;
Hoffmann, Ch. ;
Leschhorn, A. ;
Luecke, M. .
PHYSICAL REVIEW E, 2010, 82 (01)
[42]   Three-dimensional modes of fiber suspensions in the Taylor-Couette flow [J].
Department of Hydraulic and Ocean Engineering, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310028, China ;
不详 ;
不详 .
J. Donghua Univ., 2007, 1 (57-63)
[43]   Stability of Taylor-Couette and Dean flow: A semi-analytical study [J].
Deka, R. K. ;
Paul, A. .
APPLIED MATHEMATICAL MODELLING, 2013, 37 (04) :1627-1637
[44]   Synthesis of Micro-/Nanohydroxyapatite Assisted by the Taylor-Couette Flow Reactor [J].
Wang, Boyin ;
Tao, Shengyang .
ACS OMEGA, 2022, 7 (48) :44057-44064
[45]   The stably stratified Taylor-Couette flow is always unstable except for solid-body rotation [J].
Park, Junho ;
Billant, Paul .
JOURNAL OF FLUID MECHANICS, 2013, 725 :262-280
[46]   Nonlinear evolution of magnetorotational instability in a magnetized Taylor-Couette flow: Scaling properties and relation to upcoming DRESDYN-MRI experiment [J].
Mishra, Ashish ;
Mamatsashvili, George ;
Stefani, Frank .
PHYSICAL REVIEW FLUIDS, 2023, 8 (08)
[47]   Connections between centrifugal, stratorotational, and radiative instabilities in viscous Taylor-Couette flow [J].
Leclercq, Colin ;
Nguyen, Florian ;
Kerswell, Rich R. .
PHYSICAL REVIEW E, 2016, 94 (04)
[48]   Polymer solutions in co-rotating Taylor-Couette flow without vorticity [J].
Zell, A. ;
Wagner, C. .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2012, 391 (03) :464-473
[49]   Pulsed Taylor-Couette flow in a viscoelastic fluid under inner cylinder modulation [J].
Riahi, Mehdi ;
Aniss, Said ;
Touhami, Mohamed Ouazzani ;
Lami, Salah Skali .
EUROPEAN PHYSICAL JOURNAL PLUS, 2015, 130 (12) :1-13
[50]   Taylor-Couette flow of polymer solutions with shear-thinning and viscoelastic rheology [J].
Cagney, Neil ;
Lacassagne, Tom ;
Balabani, Stavroula .
JOURNAL OF FLUID MECHANICS, 2020, 905